Abstract

The interaction of a light pulse with reflective and either a passive, lossy medium or an active medium with population inversion gives rise to elastic waves, already as a result of the change in the momentum carried by the incident light. We derived a 1D analytic displacement field that quantitatively predicts the shape and amplitude of such waves in semi-infinite and finite elastic rods in a half-space and infinite layer. The results are compatible with the conservation of momentum and energy of the light-matter system. They can be used as a signature for direct measurements of the radiation-pressure-induced elastic waves and to clarify the Abraham–Minkowski momentum dilemma.

© 2013 Optical Society of America

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References

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  2. A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2013).
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  5. K. Dholakia and T. Čižmar, Nat. Photonics 5, 335 (2011).
    [CrossRef]
  6. T. Požar, P. Gregorčič, and J. Možina, Opt. Express 17, 22906 (2009).
    [CrossRef]
  7. M. Mansuripur, Opt. Commun. 283, 1997 (2010).
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  8. T. Požar and J. Možina, in Fundamentals of Picoscience, K. D. Sattler, ed. (Taylor & Francis, to be published 2013).
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    [CrossRef]

2013

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2013).
[CrossRef]

2011

K. J. Webb and Shivanand, Phys. Rev. E 84, 057602 (2011).
[CrossRef]

K. Dholakia and T. Čižmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

2010

2009

1994

J. Možina and M. Dovč, Mod. Phys. Lett. B 8, 1791 (1994).
[CrossRef]

1963

R. M. White, J. Appl. Phys. 34, 3559 (1963).
[CrossRef]

1901

P. Lebedew, Ann. Phys. 311, 433 (1901).
[CrossRef]

Cižmar, T.

K. Dholakia and T. Čižmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

Dholakia, K.

K. Dholakia and T. Čižmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

Dogariu, A.

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2013).
[CrossRef]

Dovc, M.

J. Možina and M. Dovč, Mod. Phys. Lett. B 8, 1791 (1994).
[CrossRef]

Fainman, Y.

Gregorcic, P.

Lebedew, P.

P. Lebedew, Ann. Phys. 311, 433 (1901).
[CrossRef]

Mansuripur, M.

M. Mansuripur, Opt. Commun. 283, 1997 (2010).
[CrossRef]

Mizrahi, A.

Možina, J.

T. Požar, P. Gregorčič, and J. Možina, Opt. Express 17, 22906 (2009).
[CrossRef]

J. Možina and M. Dovč, Mod. Phys. Lett. B 8, 1791 (1994).
[CrossRef]

T. Požar and J. Možina, in Fundamentals of Picoscience, K. D. Sattler, ed. (Taylor & Francis, to be published 2013).

Požar, T.

T. Požar, P. Gregorčič, and J. Možina, Opt. Express 17, 22906 (2009).
[CrossRef]

T. Požar and J. Možina, in Fundamentals of Picoscience, K. D. Sattler, ed. (Taylor & Francis, to be published 2013).

Saenz, J. J.

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2013).
[CrossRef]

Shivanand,

K. J. Webb and Shivanand, Phys. Rev. E 84, 057602 (2011).
[CrossRef]

Sukhov, S.

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2013).
[CrossRef]

Webb, K. J.

K. J. Webb and Shivanand, Phys. Rev. E 84, 057602 (2011).
[CrossRef]

White, R. M.

R. M. White, J. Appl. Phys. 34, 3559 (1963).
[CrossRef]

Ann. Phys.

P. Lebedew, Ann. Phys. 311, 433 (1901).
[CrossRef]

J. Appl. Phys.

R. M. White, J. Appl. Phys. 34, 3559 (1963).
[CrossRef]

Mod. Phys. Lett. B

J. Možina and M. Dovč, Mod. Phys. Lett. B 8, 1791 (1994).
[CrossRef]

Nat. Photonics

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2013).
[CrossRef]

K. Dholakia and T. Čižmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

Opt. Commun.

M. Mansuripur, Opt. Commun. 283, 1997 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

K. J. Webb and Shivanand, Phys. Rev. E 84, 057602 (2011).
[CrossRef]

Other

T. Požar and J. Možina, in Fundamentals of Picoscience, K. D. Sattler, ed. (Taylor & Francis, to be published 2013).

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Figures (3)

Fig. 1.
Fig. 1.

Displacement of the semi-infinite rod’s front plane as a function of time: reflection plus absorption [Eq. (8) + Eq. (9); upper four, black curves] and reflection plus gain [Eq. (8) + Eq. (10); lower four, red curves]. The impulse response has a sharp initial step. The response to i ( t ) as given in Eq. (11) with t ˜ 0 = 0.5 is smooth. Parameters: T = 0.5 and x ˜ 0 = ln 4 or x ˜ 0 .

Fig. 2.
Fig. 2.

Displacement of the semi-infinite rod’s cross-section far from the front plane as a function of the retarded time. The graph legend is the same as in Fig. 1.

Fig. 3.
Fig. 3.

Motion of the finite rod of length x ˜ 0 ( u ˜ = Γ ˜ R A ) . Red: front plane [ u ˜ ( x ˜ = 0 ) ], Blue: middle cross-section [ u ˜ ( x ˜ = 0.5 x ˜ 0 ) ], Black: end plane [ u ˜ ( x ˜ = x ˜ 0 ) ], Gray: center of mass [ u ˜ * ; Eq. (18)]. Dashed line: total reflection ( T = 0 ). Solid line: half-reflection ( T = 0.5 ). Parameters: x ˜ 0 = ln 4 and i ˜ ( t ˜ ) = δ ( t ˜ ) .

Equations (18)

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u ¨ ( x , t ) = c 0 2 u ( x , t ) + f ( x , t ) ρ 1 ,
u ( x , 0 ) = 0 and v ( x , 0 ) = 0 ,
σ ( 0 , t ) = E u ( 0 , t ) = P ( t ) and lim x u ( x , t ) = 0 .
u ( 0 , t ) = 2 R ( ρ c 0 2 c ) 1 i ( t ) ,
f ( x , t ) = ± T μ c 1 e μ x H ( x 0 x ) i ( t ) .
t ˜ j = μ c 0 t j , x ˜ j = μ x j , u ˜ j = u L 1 u j = ρ c 0 c q 1 u j , v ˜ = ρ c ( q μ ) 1 v , σ ˜ = c ( μ c 0 q ) 1 σ , i ˜ = ( μ c 0 q ) 1 i , G ˜ j = ρ c 0 c G j , B ˜ j = ρ c 0 c B j , Γ ˜ j = ρ c 0 c Γ j ,
u ˜ ( x ˜ , t ˜ ) = G ˜ ( x ˜ , t ˜ ) * i ˜ ( t ˜ ) = 0 t ˜ G ˜ ( x ˜ , ξ ) i ˜ ( t ˜ ξ ) d ξ .
G ˜ R = 2 R H ( t ˜ x ˜ )
G ˜ A = T H ( x ˜ t ˜ ) ( e x ˜ sinh ( t ˜ ) + [ 1 cosh ( t ˜ x ˜ ) ] H [ t ˜ ( t ˜ x ˜ ) ] + 0.5 ( e ( t ˜ x ˜ ) e x ˜ 0 ) H [ t ˜ ( t ˜ x ˜ x ˜ 0 ) ] + 0.5 ( e ( t ˜ + x ˜ ) e x ˜ 0 ) H [ t ˜ ( t ˜ + x ˜ x ˜ 0 ) ] { e x ˜ sinh ( t ˜ ) 0.5 ( e t ˜ x ˜ e x ˜ 0 ) H [ t ˜ ( t ˜ x ˜ + x ˜ 0 ) ] + 0.5 ( e ( t ˜ + x ˜ ) e x ˜ 0 ) H [ t ˜ ( t ˜ + x ˜ x ˜ 0 ) ] } H [ t ˜ ( x ˜ x ˜ 0 ) ] ) ,
G ˜ G ( x ˜ , t ˜ , x ˜ 0 ) = G ˜ A ( x ˜ , t ˜ , x ˜ 0 ) .
i ( t ) = q ( t / t 0 2 ) e t / t 0 .
σ ˜ R max = 2 ( 1 T ) ( e t ˜ 0 ) 1 .
G ˜ A ( x ˜ = 0 ) = T { ( 1 e t ˜ ) ; 0 t ˜ < x ˜ 0 ( 1 e x ˜ 0 ) ; x ˜ 0 t ˜ .
G ˜ A ( x ˜ ) = T 2 { 0 ; τ ˜ < x ˜ 0 ( e τ ˜ e x ˜ 0 ) ; x ˜ 0 τ ˜ < 0 [ 2 ( e τ ˜ + e x ˜ 0 ) ] ; 0 τ ˜ < x ˜ 0 2 ( 1 e x ˜ 0 ) ; x ˜ 0 τ ˜ .
Γ ˜ R A ( x ˜ , t ˜ , x ˜ 0 ) = C F B ˜ R ( x ˜ , t ˜ , x ˜ 0 ) + C B B ˜ R ( x ˜ 0 + x ˜ , t ˜ , x ˜ 0 ) + C A F B ˜ A ( x ˜ , t ˜ , x ˜ 0 ) + C A B B ˜ A ( x ˜ 0 + x ˜ , t ˜ , x ˜ 0 ) ,
C F = 1 T R Δ , C B = T e x ˜ 0 Δ , C A F = e 2 x ˜ 0 Δ , C A B = R e x ˜ 0 Δ , where Δ = ( e 2 x ˜ 0 R 2 ) 1 .
B ˜ k ( x ˜ , t ˜ , x ˜ 0 ) = n = 0 [ G ˜ k ( x ˜ , t ˜ 2 n x ˜ 0 ) + G ˜ k ( 2 x ˜ 0 x ˜ , t ˜ 2 n x ˜ 0 ) ] ,
u ˜ * = { 2 + [ ( 1 + e x ˜ 0 ) 1 T 1 ] 1 } t ˜ / x ˜ 0 ,

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